The concepts of frequency response and power spectrum are extended to the general problem of determining the statistics of the response of an arbitrary space-dependent, time-dependent, linear system subjected to a multidimensional nonhomogeneous, nonstatlonary, random field„ This represents the most complex (statistically) type of loading that could be encountered. Previous research with regard to linear systems subjected to random loads has always been less general, that is, the investigators have placed restrictions on the system, the input or both, it is shown that these are really special cases of the general problem and their results may be easily derived from the resulting general expressions, This material is covered in the first three chapters.

Throughout the dissertation emphasis is placed on obtaining response statistics that would be of Interest to engineers concerned with design problems, Chapter Four presents a method for obtaining two statistical parameters of a continuous nonstatlonary function representing the response of a system, which would be of interest in determining the probability of failure of the system. These are:​

1. the probability P_α(t)dt that the nonstatlonary random function q(t), subject to q(0)=0, exceeds the value q(t)=α for the first time in the interval t, t+dt.
2. the probability R_α(t)dtdα that the nonstatlonary random function q(t) has a maximum (minimum) between the values _α, _α+d_α in the interval t, t+dt.

The first is related to the probability of failure of the system through exceedence of an allowable stress and the second to the probability of failure through reversals or cycling of stresses.

Finally,the results of the analysis derived in the first four chapters are applied to problems associated with the response of launch vehicles to wind fields0 A method is presented by which it is possible to compute load statistics and, ultimately, the probability of survival of the vehicle as it rises through the atmosphere, whether the system is linear or not e in the case where the system is linear, several methods are proposed by which the load statistics may be computed directly from a knowledge of the wind statistics and the system equations. One of the proposed methods is then applied to the problem of obtaining a preliminary estimate of the maximum bending moment induced in a typical launch vehicle as it ascends through the atmosphere at Cape Kennedy.